Quantum Statistical Physics and Field Theory

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4-state Potts model;re

Main Topics

Statistical Mechanics

  • Basic postulates
  • Ensembles
  • Density matrix
  • Indistinguishable particles
  • Bose-Einstein and Fermi-Dirac statistics
  • Chandrashekar limit
  • Anyons

Phase transitions

  • Symmetry and order parameters
  • Critical exponents and scaling laws
  • Lattice models and continuum limit

Bi-dimensional lattice models

  • Duality of the Ising model
  • Combinatorial solutions
  • Transfer matrix and Yang-Baxter equations
  • Bethe Ansatz
  • Potts model, random walks and self-avoiding walks

Field Theory Approach to Critical Phenomena

  • Feynman rules
  • Wick theorem
  • S-matrix
  • Unitarity and crossing equations
  • N-particle phase space, asymptotic and threshold behavior
  • Euclidean Quantum Field Theories
  • Path integral

Renormalization Group

  • Effective Hamiltonians
  • Running coupling constants and beta functions
  • Fixed points and scaling region
  • Relevant, irrelevant and marginal operators

Fermionic formulation of the 2-dimensional Ising model

  • Order and disorder operators
  • Operator product expansion and fermionic fields
  • Dirac equation

Conformal Field Theory

  • Conformal Invariance
  • Ward identity and primary fields
  • Virasoro algebra and central charge
  • Representation theory
  • Casimir effect and other finite size phenomena
  • Bosonic and fermionic fields

Minimal models

  • Differential equations of the correlation functions
  • Gas di Coulomb
  • Modular invariance
  • Statistical Models with Supersymmetry
  • Parafermionic and Wess-Zumino-Witten models

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